Big Idea:
Students want to flip numbers to make subtraction easier. Work with manipulatives and drawings to understand why flipping doesn't make sense.

I have students hand out the math tool suitcases (we have created suitcases to carry all of our strategies for addition and subtraction). I ask students to take out their math journals. I tell them to look at what I have put on the board and copy the problems onto their paper:

9 - 3 = 6

8 - 6 = 2

6 - 9 = 3

7 - 5 = 2

4 - 9 = 5

I ask them to put a check mark next to all the problems that are correct. Once everyone has completed that, I ask students to raise their hands if they think each problem that I point to is correct.

Once we have looked at the votes, I ask students to draw each problem with circles by drawing the first number and crossing out the second number. Does anyone want to change any of their votes? I tell them to mark the problems again and then we raise our hands again.

Why did some of you change your votes? (You can't take a bigger number from a smaller number is what I am looking for kids to discover here, but if no one suggests that, I will bring students to the rug, give them snap blocks and have them start with a smaller number that I write on the board, and then try to take away the larger number to see if it works. Here the students will see concretely that you don't have enough.)

Once I am sure students have an idea about what I am talking about, I will introduce the idea of NO FLIPPING. I will show them a person standing on their heads with an X across the picture. I tell them that we must remember that for subtraction as well.. NO FLIPPING! I will draw a subtraction problem trying to flip over with an X through it as a reminder.

I give students a large piece of paper. I ask them to fold the paper in half the long way. Now fold the paper in half the short way 2 times to give 8 separate areas. I ask students to trace the folds so they can see the separate work areas.

Ok, now we are going to practice NO FLIPPING SUBTRACTION. I ask them to look at the problem 21 - 17 written vertically on the board. In the first square I want you to make a ten's and one's house (place value mat in the shape of a house) and draw 21 upstairs using tens rods in the ten's place and ones cubes in the ones place. I demonstrate on the board what I expect students to do. (I want to make sure they see what we are doing.) I check that everyone has drawn the number correctly. I am expecting students to model the problem with mathematics by drawing the blocks (MP4)

OK, now we are going to try to take 17 away from that 21 we just drew. We are going to start at the one's house. How many are there (1).. oh no.. how many do we need to take away (7). Well we can't and we can't flip because it says.. NO FLIPPING.. oh no. I guess we just give up... Right?.. Well what can we do? (borrow from next door).

Let's ask the 20 next door if we can borrow ten. (I pretend to knock at the door and ask if I can borrow ten.) Then I bring ten over and say.. well now that you are in the ones, I have to separate you into ones. I draw ten ones next to the one already there.

HMM.. now can I subtract without flipping? YEAH! Let's do it. Can you all borrow ten from next door? How many tens are left? (1) ok now separate that ten into ones and let them move into the ones house.

Great, now lets subtract our 17. What is left? (4).

I go through the process with students several more times. We are working together to scaffold their learning. They will work independently after I feel that students are secure with the NO FLIPPING rule.

Resources (2)

Resources

I have a practice page with 6 double-digit subtraction problems on it.subtraction practice.docx I have created the houses for subtraction and left room for students to draw their blocks. I have each student complete the paper independently. I circulate around the room to support students who may be struggling with the problems. I want to help students make sense of the problems and persevere to solve them even though subtraction is not always easy (MP1).

Big Idea:
This lessons starts with a concrete representation of a change unknown problem and then pushes students to think abstractly and develop number sentences to solve change unknown word problems.